The Easter Road side have had a poor run of form recently, picking up five points from a possible 24, and winning just once, a 2-1 win over Livingston.
Back-to-back losses at home to Morton and away to Dumbarton effectively ended any lingering hopes Hibs had of catching Rangers but recent results, including surrendering a two-goal lead to 10-man Falkirk has seen Hibs falter in the race for second place.
But Dempster has given her full support to Stubbs, who takes his side to Hampden on Saturday as Hibs look to reach their second final of the season.
“We’ve hit a dip in form,” Dempster told the BBC. “Alan is supported and we’re going forward. We’re in here for the long game.”
Dempster, who shook things up when she arrived in the summer following Hibernian’s relegation to the Championship, still believes the Easter Road side can win promotion back to the top flight.
She added: “We haven’t become poor overnight. We’re in the Scottish Cup semi-final, we got to the League Cup final and we can get promoted this season.
“We can do things this season.”
And the former Motherwell chief praised Stubbs, who took the reins at Easter Road following the departure of Terry Butcher.
Dempster said: “Alan is keeping the dressing room positive, training is good and he’s pulling us all together. That’s what we need here.”
Describing the club’s recent dip as ‘a poor bit of form’, Dempster stressed that the club has had a good season and didn’t want to ‘over-dramatise things’.
She continued: “People are upset, they’re hurting. They don’t want to be losing these games. But you’re under pressure working at Hibernian. We’re all under pressure and Alan handles that really well.”
Dempster also revealed that she has considered the prospect of Hibs facing a third season in the second tier, adding: “I’m the chief executive, I need to have a long-term plan.
“But I’m not even considering that at the moment. I’m focused on promotion. We’re focused on the Scottish Cup this weekend.”
Hibs take on Dundee United at Hampden on Saturday for a place in the Scottsh Cup final.